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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font> holds <br/> ( <font color="Olive" title="b2">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</font></span>)</span> iff  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b2">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b2">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Olive" title="b1">x</font></span>)</span> #) )</span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> iff  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #) )</span><br/>



<a NAME="E1:106"/><i><font color="Green" title="E63">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="ref" href="tex_4.html#D17" target="_self" title="TEX_4:def.17">Def17</a></i>;<br/>
<b>thus </b><a NAME="E2:106"/>
( <font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> implies  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #) )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #) implies <font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:106_1"/>
<font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #)</span><br/>

<a NAME="E2:106_1"/><b>then </b>
 <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tex_4.html#K2" title="TEX_4:func.2">MaxADSet</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="tex_4.html#E1:106"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E3:106_1"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #)
 <b>by </b><i><a class="txt" href="tex_4.html#E1:106"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:106"/>
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span></span><br/>

<b>hence </b><a NAME="E4:106"/>
<font color="Maroon" title="c3">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="tex_4.html#K5" title="TEX_4:func.5">MaxADSspace</a> <font color="Maroon" title="c2">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="tex_4.html#E1:106"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="tex_4.html#T23" target="_self" title="TEX_4:th.23">Th23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
